Calculation of absolute diffusion rates in oxides

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Abstract
The authors have calculated the absolute rate of diffusion for Mg2+ and Fe3+ ions in MgO using atomistic modelling. The calculations use a shell model, incorporating tested interatomic potentials, and exploit recent advances in computer codes. The agreement is extremely good where experimental data are available for comparison. For Mg2+ in MgO at 1400 degrees C they predict a pre-exponential factor of 32.9 THz using simple Vineyard theory (experiment 18+or-7 THz after correction for the important volume dependence of the activation energy) and an activation energy of 2.26 eV (experiment 2.3+or-0.2 eV). Close inspection of the energy changes for displacements from the saddle point normal to the jump path shows that within kT of the saddle point energy there are significant departures from the harmonic dependence required for validity of Vineyard theory. Corrections by both analytical methods and numerical integration improve agreement with experiment, predicting 23-25 THz overall. For Fe3+ much slower diffusion is predicted even though the jump path bifurcates to give two saddle points. The authors do not predict the rapid Fe3+ motion reported in aggregation experiments and conclude that other mechanisms are involved. They have also used the dynamical theory of Rice and Slater which gives similar, but by no means identical, predictions for the diffusion rates.